If Philip's utility function is U=4 (41)05+42 what are his demand functions for the two goods? Let the price of q, be p,, let the price of a, be p2, and let income be Y. Philip's demand for q, as a function of p, and p, is and his demand for good q, is 92 = %3D (Properly format your expressions using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscripto

Consider the following Marshallian Demand Function derived from the utility maximization problem, X = a M P where X is the quantity consumed, Mis income of the consumer, P is the price of the good, and α is some number between 0 and 1 which represents the relative importance of the good. Does this demand function satisfy the law of demand? (_ Why or why not? (*

Let U(x, y) = 3x + y be the utility function of a consumer, whohas a budget of I. As a function of I, find the consumer’s Walrasian demand when the prices are px = py = 1. The price of good x increases to 2, find the new Walrasian demand for the new prices px = 2 and py = 1. Decompose this change into an income and a substitution effect.

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(2) Lisa can buy either whole chickens or chicken wings at her local supermarket. Her utility function over whole chickens and chicken wings is U(xc,Xw) = 2xc + Xw, where x, and xw are chickens and chicken wings, respectively. What is her demand function xc (pc, Pw, m) for chickens?

Suppose your utility for goods x1 and x2 is represented by the following utility function:  U(x1,x2)= x11/5  x24/5 a) What is your marginal rate of substitution, MRS12? b)  If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25?   PLEASE ONLY ANSWER PART C, D AND E

Suppose the demand curves for goods A, B, and C have the following functional forms, where Q denotes quantity demanded, P denotes price, and M denotes income: QA = 120 - 3.5PA - 6PB + 14M QB = 100 - 2PB + 3PC + 1.1M Qc = 1500 -0.5Pc - 300M. Based on these demand curves, which of the following goods are known to be normal goods? A, B and C B A and B only C A

(In this question we denote income by Y, not by W as in the lecture notes). The following figure shows the consumption of x and y for two market situations. We can conclude that: x is a normal good for all market situations. py is greater than px. It is not conclusive. x is an inferior good for some market situation. y is an inferior good for some market situation.

Based on Nick's willingness to sell, plot his supply curve as a step function on the following graph using the orange points (square symbol). Be sure to plot your first point at (0, 0). Price of Water 10 9 100 8 7 8 10 3 2 1 0 0 2 3 Quantity of Water Suppose the price of a bottle of water is $4. In this case, Nick receives $ 5 If the price rises to $6, Nick now sells Nick's Supply Price = $4 Use the black line (plus symbol) to draw a price line at $4. Next use the grey point (star symbol) to indicate how many bottles of water Nick will produce and sell at that price. Finally, use the purple point (diamond symbol) to shade the area that represents Nick's producer surplus. bottles of water. This Quantity Sold Producer Surplus in producer surplus from his water sales. his producer surplus to $

Suppose that i's preferences over goods x and y are represented by the following utility function U₁(x, y)=x45¹5. Let m denote the consumer's income, p denote the price of good x and let the price of good y equal 1. A) Find the Marshallian demand functions for goods x and y. B) Show how each of the demand function is affected by a change in the price of good x. C) Which of the goods is an inferior good?